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Saturday, December 22, 2007

Winter Solstice

Today is the Winter Solstice, the shortest day of the year in the Northern Hemisphere. At 06:08 UT (1:08 AM EST, 07:08 MEZ), the Sun will reach its southern turning point on the celestial sphere, culminating above some point in the Indian Ocean on the Tropic of the Capricorn. In Frankfurt am Main, Germany, sunrise will be at 08:22, and sunset at 16:26, yielding in principle 8 hours and 4 minutes of sunshine.

Today's plot shows the time of sunrise, Sun's culmination, and sunset for Frankfurt over the course of the year. Date is on the horizontal axis, and time of the day on the vertical axis. The shortest day is marked by the vertical line. Sunrise and sunset are shown in orange, culmination - that is, "the true noon", when the Sun is exactly at South - in red. The lines in black, purple, and blue mark the times of astronomical, nautical, and civil twilight, respectively, when the Sun is 18°, 12°, and 6° below the horizon.

Besides the changes in the length of the day, which is roughly between 8 and 16 hours over the course of the year, the plot shows one more unexpected phenomenon: The time of the culmination of the Sun, the true Noon, is not always at the same time - it varies by about half an hour over the year. As a result, the time span of daylight not only varies in length, but also shifts around slightly with respect to the hours of the day. The difference between true Noon and the time when one would expect the Sun at South from the longitude (the "mean Noon", 12:25 MEZ for Frankurt at 8°41 East, for example) is called the Equation of Time. It is caused by the combined effect of the elliptical shape of the Earth's orbit and the tilt of the Earth's axis.

As a side effect of the Equation of Time, the earliest sunset is not at the Winter Solstice, but a few days before. The figure on the left shows a detail of the plot above: Sunrise, culmination, and sunset between November and February. One can see clearly that there is an offset of about 15 days between the earliest sunset, around mid-December, and the latest sunrise, in the first days of January.

The rapid shift in the time of culmination - about half an hour between beginning of November and end of January - can be understood from the fact that the Earth is at the perihelion, the smallest distance to the Sun on its orbit, around January 3. As described by Kepler's law of areas, encoding the conservation of angular momentum, the Earth's angular velocity as seen from the Sun is biggest at the perihelion. But this means that the Earth has to spin a little bit longer from culmination to culmination than at other phases of the orbit. As a consequence, culmination is always a little late from day to day, and the "true Noon" shifts from a bit later than 12 o'clock to 12:40 between November and February. Summer days, instead, will be a little bit shorter.

But at the meantime, those of us in the Northern Hemisphere who are suffering from the winter's darkness can look forward to the daylight coming back.